I am reading some papers wherein a wireless channel is assumed as zero mean circularly symmetric complex Gaussian (ZMCSCG) with unit variance and it is also mentioned that the channel undergoes Rayleigh Fading. I am confused due to this two different distributions. I mean can we assume like this that is "ZMCSCG and Rayleigh Fading together"

Note: I know from basic statistics that absolute value of standard complex gaussian denotes Rayleigh distribution.

Any help in this regard will be highly appreciated.

  • $\begingroup$ Please read en.wikipedia.org/wiki/Rayleigh_fading#The_model $\endgroup$
    – AlexTP
    Commented Aug 13, 2021 at 9:15
  • $\begingroup$ Thanks for your reply....Can you please tell whether the Rayleigh distribution needs to have unit variance of complex Gaussian or we can have Rayleigh distribution even if variance of complex Gaussian is not equal to 1 (i.e., other than 1)... $\endgroup$
    – paru
    Commented Aug 13, 2021 at 9:37
  • $\begingroup$ @paru doesn't have to be unit variance, otherwise it would be pretty boring. $\endgroup$ Commented Aug 13, 2021 at 9:48
  • $\begingroup$ Ok... Thanks Marcus...So what I had understood is : "Magnitude of Zero mean any variance circularly symmetric complex Gaussian represents Rayleigh random variable" . Can you please tell whether my understanding is correct or not. $\endgroup$
    – paru
    Commented Aug 13, 2021 at 9:52
  • $\begingroup$ I don't understand your understanding, sadly :( $\endgroup$ Commented Aug 13, 2021 at 13:13


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